alexsisssm alexsisssm
  • 12-05-2017
  • Mathematics
contestada

let f(7) = 0, f'(7)= 14, g(7) = 1 and g'(7) = 1/7, find h'(7) if h(x) = f(x)/g(x)

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jdoe0001 jdoe0001
  • 12-05-2017
[tex]\bf h(x)=\cfrac{f(x)}{g(x)}\impliedby \textit{let us use the quotient rule}\\\\ -----------------------------\\\\ \cfrac{dh}{dx}=\left. \cfrac{\frac{df}{dx}g(x)-f(x)\frac{dg}{dx}}{[g(x)]^2}\right|_{x=7}\quad \begin{cases}f'(7)=14\\\\ f(7)=0\\\\ g'(7)=\frac{1}{7}\\\\ g(7)=1 \end{cases}\implies \cfrac{dh}{dx}=\cfrac{14\cdot 1-0\cdot \frac{1}{7}}{[1]^2} \\\\\\ \cfrac{dh}{dx}=\cfrac{14}{1}\implies \cfrac{dh}{dx}=14 [/tex]
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